Semiflexible Fully Packed Loop Model and Interacting Rhombus Tilings

Motivated by a recent adsorption experiment [ M. O. Blunt et al. Science 322 1077 (2008)], we study tilings of the plane with three different types of rhombi. An interaction disfavors pairs of adjacent rhombi of the same type. This is shown to be a special case of a model of fully packed loops with interactions between monomers at distance two along a loop. We solve this model using Coulomb gas techniques and show that its critical exponents vary continuously with the interaction strength. At low temperature it undergoes a Kosterlitz-Thouless transition to an ordered phase, which is predicted from numerics to occur at a temperature T∼110  K in the experiments.